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#11
11-16-2007, 06:56 PM
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Re: An Interesting Physics Problem
Not at all how I solved it, but just effective.
I will say the choice of placing your axis of rotation through the point of contact seems conceptually strange to me, since the sphere is simply rotating about an axis through it's center of mass. To each his own though! 
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#12
11-16-2007, 07:09 PM
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Re: An Interesting Physics Problem
I started with energy conservation, since the negative work done by friction is equal to the positive work done by the torque due to the friction. So after a displacement x:
mgx sinq = (7/10) mv^2 Differentiating with respect to time: mgv sinq = (7/5) mva a = (5/7)g sinq Newton's 2nd Law: Fnet_x = mg sinq - F_f = ma = (5/7) mg sinq (2/7) mg sinq = F_f = mu mg cosq tanq = (7/2)mu = 7/4 In general, for a round object of moment of inertia I = cmr^2, slope = tanq = (1 + 1/c) mu Which is a neat formula.
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#13
11-16-2007, 07:33 PM
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Re: An Interesting Physics Problem
[ QUOTE ]
Not at all how I solved it, but just effective. I will say the choice of placing your axis of rotation through the point of contact seems conceptually strange to me, since the sphere is simply rotating about an axis through it's center of mass. To each his own though! [/ QUOTE ] This approach is typically taught in undergrad engineering courses as one alternative method of solving these types rigid body dynamics problems. It has the advantage that the point of contact is an instantaneous inertially fixed axis of rotation, which can simplify some problems that have a center of mass which is both translating and rotating, like the one you posted.
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#14
11-16-2007, 07:36 PM
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Re: An Interesting Physics Problem
[ QUOTE ]
[ QUOTE ] Not at all how I solved it, but just effective. I will say the choice of placing your axis of rotation through the point of contact seems conceptually strange to me, since the sphere is simply rotating about an axis through it's center of mass. To each his own though! [/ QUOTE ] This approach is typically taught in undergrad engineering courses as one alternative method of solving these types rigid body dynamics problems. It has the advantage that the point of contact is an instantaneous inertially fixed axis of rotation, which can simplify some problems that have a center of mass which is both translating and rotating, like the one you posted. [/ QUOTE ] Yeah, that makes sense. In fact I probably learned that 15 years ago. Bit decay. [img]/images/graemlins/frown.gif[/img]
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